Probability
Basic probability and set operations
Grade None
Question:
<p>In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is:</p>
<p>\(\dfrac{1}{3}\)</p>
<p>\(\dfrac{1}{6}\)</p>
<p>\(\dfrac{3}{4}\)</p>
<p>\(\dfrac{5}{6}\)</p>
Step-by-Step Solution
Key Concept: Use the principle of inclusion-exclusion to find students opting for at least one activity, then subtract from total to find those opting for neither.
<p><strong>Step 1:</strong> Find total students who opted for at least one activity using inclusion-exclusion.</p><p>Students opting for NCC or NSS = |NCC ∪ NSS| = |NCC| + |NSS| - |NCC ∩ NSS|</p><p>= 40 + 30 - 20 = 50 students</p><p><strong>Step 2:</strong> Find students opting for neither NCC nor NSS.</p><p>Students opting for neither = Total students - Students opting for at least one</p><p>= 60 - 50 = 10 students</p><p><strong>Step 3:</strong> Calculate the probability.</p><p>P(neither NCC nor NSS) = 10/60 = 1/6</p><p>∴ Answer: B</p>
Correct Answer: B